pith. sign in

arxiv: 2605.21315 · v1 · pith:ZT2ISLRTnew · submitted 2026-05-20 · ✦ hep-ph · hep-ex

Statistical sensitivity of neutrinoless double-beta decay exchange mechanism discrimination by tracking experiments

Jason Detwiler , Ke Han , Tao Li This is my paper

Pith reviewed 2026-05-21 03:41 UTC · model grok-4.3

classification ✦ hep-ph hep-ex
keywords neutrinoless double-beta decayexchange mechanismtracking detectorsstatistical sensitivityelectron energy reconstructionopening anglebackground rejection
0
0 comments X

The pith

Reconstruction of electron energies and opening angles allows neutrinoless double-beta decay mechanism discrimination with only a few well-reconstructed events.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows that if one beyond-Standard-Model exchange mechanism dominates neutrinoless double-beta decay, the distributions of the two electrons' energies and their opening angle carry enough information to identify which mechanism is at work. This discrimination reaches 1 sigma significance with just a handful of clean events and climbs to 3 sigma with roughly 10 events. Even after folding in realistic detector resolution uncertainties the requirement rises only to about 25 events, provided backgrounds stay low enough for clean event selection. The finding matters for experiments designed around discovery sensitivity, because those typically expect only a small number of signal counts yet can still extract mechanism information without waiting for high statistics.

Core claim

If a single mechanism dominates the neutrinoless double-beta decay process, reconstruction of the individual energies and the opening angle between the emitted electrons allows its discrimination at the 1σ level with just a few well-reconstructed events. Only approximately 10 such events are required to reach 3σ-level discovery sensitivity. In the presence of realistic reconstruction uncertainties this requirement increases to approximately 25 events, indicating that substantial discrimination power is retained as long as backgrounds remain small.

What carries the argument

Statistical discrimination power arising from the joint distribution of reconstructed electron energies and their opening angle for events from neutrinoless double-beta decay.

Load-bearing premise

The analysis assumes that backgrounds remain small enough that signal events can be cleanly selected and that the modeled reconstruction uncertainties accurately represent real detector performance without additional unaccounted systematics.

What would settle it

A data set in which 25 well-reconstructed events from a known single mechanism yield no statistically significant preference for that mechanism over alternatives once all modeled uncertainties are included.

Figures

Figures reproduced from arXiv: 2605.21315 by Jason Detwiler, Ke Han, Tao Li.

Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 1
Figure 1. Figure 1: FIG. 1. Ideal 2D probability distributions for [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Discovery probability vs. number of events for varying [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Reconstructed 2D probability distributions for [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Discovery probability vs. number of events for various [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
read the original abstract

Reconstruction of the individual energies and the opening angle between the electrons emitted in neutrinoless double-beta decay can probe the nature of the beyond-the-Standard-Model exchange mechanism that underlies the process. Although it is often stated that discrimination of the mechanism would require such measurements to be performed with high statistics, we show that this is not the case. If a single mechanism dominates the process, its discrimination at the 1$\sigma$ level is already achieved with just a few well-reconstructed events; only $\sim$10 such events are required to reach 3$\sigma$-level discovery sensitivity. In the presence of realistic reconstruction uncertainties, this requirement increases to $\sim$25 events, indicating that substantial discrimination power is retained as long as backgrounds remain small. We conclude that the pursuit of tracking detectors for exchange-mechanism discrimination remains valuable even for ``discovery-class'' experiments in which only a few signal counts are expected.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The manuscript performs a statistical study of how well the energy and angular distributions of electrons from neutrinoless double-beta decay can discriminate between different beyond-Standard-Model exchange mechanisms in a tracking detector. It concludes that, assuming a single mechanism dominates and backgrounds are small, a handful of well-reconstructed events already yield 1σ separation, roughly 10 events reach 3σ discovery sensitivity, and this rises only to ~25 events once realistic Gaussian reconstruction uncertainties are included.

Significance. If the modeling assumptions are validated, the result is useful: it supplies concrete, low event-count thresholds that show tracking information retains substantial discriminating power even in the low-statistics regime expected for a first discovery. This directly informs the design trade-offs for next-generation 0νββ experiments that incorporate tracking.

major comments (1)
  1. [Abstract] Abstract and concluding section: the central claim is conditioned on backgrounds remaining 'small' and on the modeled reconstruction uncertainties accurately representing real detector performance, yet no quantitative threshold for acceptable background contamination nor any degradation curve versus background rate is provided. This assumption is load-bearing; even O(1) background events mixed into the sample would alter the observed energy-angle distributions and reduce the quoted separation power.
minor comments (2)
  1. [Methods] The manuscript would benefit from an explicit statement of the likelihood or test statistic used to quantify the separation between mechanisms (e.g., whether a binned likelihood ratio or a Kolmogorov-Smirnov test on the two-dimensional distributions is employed).
  2. [Results] Figure captions should state the exact number of simulated events and the precise values of the energy and angular resolution parameters adopted for the 'realistic uncertainties' case.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the positive assessment of the work's significance and for the constructive major comment. We address it directly below and agree that a quantitative treatment of background effects will strengthen the manuscript.

read point-by-point responses

  1. Referee: [Abstract] Abstract and concluding section: the central claim is conditioned on backgrounds remaining 'small' and on the modeled reconstruction uncertainties accurately representing real detector performance, yet no quantitative threshold for acceptable background contamination nor any degradation curve versus background rate is provided. This assumption is load-bearing; even O(1) background events mixed into the sample would alter the observed energy-angle distributions and reduce the quoted separation power.

    Authors: We agree that the assumption of small backgrounds is load-bearing for the quoted sensitivities and that the manuscript would benefit from a quantitative threshold or degradation curve. In the revised version we will add a new subsection and figure that explicitly shows the required event counts for 1σ and 3σ mechanism discrimination as a function of background contamination fraction. Background events will be drawn from a conservative distribution (flat in energy and opening angle) and mixed into the signal sample; the full likelihood analysis will then be repeated to produce the requested degradation curve. This will allow readers to judge acceptable background levels directly. Regarding reconstruction uncertainties, the Gaussian smearing parameters are taken from representative tracking-detector resolutions reported in the literature; we will add a short clarifying paragraph stating that these are illustrative and that actual performance may differ, while noting that the main result already includes a realistic-uncertainty case that raises the requirement from ~10 to ~25 events. revision: yes

Circularity Check

0 steps flagged

No circularity: sensitivity estimates from standard statistical separation of simulated distributions

full rationale

The paper derives its event-count thresholds for 1σ and 3σ mechanism discrimination by computing the statistical separation power between modeled energy-angle distributions for different exchange mechanisms, first in the ideal case and then after convolution with stated Gaussian reconstruction uncertainties. This procedure uses conventional likelihood or hypothesis-testing methods applied to Monte Carlo samples and does not reduce any claimed prediction to a fitted parameter, a self-referential definition, or a load-bearing self-citation whose validity is presupposed inside the present work. The explicit caveat that backgrounds must remain small is an external modeling assumption rather than an internal definitional loop; the derivation therefore remains self-contained against external statistical benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard statistical discrimination applied to simulated electron distributions under the assumption that one mechanism dominates and that detector response can be modeled with realistic but unspecified uncertainties.

free parameters (1)
  • energy and angular resolution parameters
    Values chosen to represent realistic tracking-detector performance; not derived from first principles within the paper.
axioms (2)
  • domain assumption Single mechanism dominates the decay
    The discrimination power calculation assumes one exchange mechanism is responsible for all events.
  • domain assumption Backgrounds remain small
    The quoted sensitivities hold only when signal events can be selected with negligible background contamination.

pith-pipeline@v0.9.0 · 5690 in / 1270 out tokens · 39367 ms · 2026-05-21T03:41:50.486641+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

29 extracted references · 29 canonical work pages · 7 internal anchors

  1. [1]

    Agostini, G

    M. Agostini, G. Benato, J. A. Detwiler, J. Men´ endez, and F. Vissani, Toward the discovery of matter creation with neutrinolessββdecay, Rev. Mod. Phys.95, 025002 (2023), arXiv:2202.01787 [hep-ex]

    work page arXiv 2023

  2. [2]

    A neutrinoless double beta decay master formula from effective field theory

    V. Cirigliano, W. Dekens, J. de Vries, M. L. Graesser, and E. Mereghetti, A neutrinoless double beta decay mas- ter formula from effective field theory, JHEP12, 097, arXiv:1806.02780 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv

  3. [3]

    Weinberg, Baryon and Lepton Nonconserving Pro- cesses, Phys

    S. Weinberg, Baryon and Lepton Nonconserving Pro- cesses, Phys. Rev. Lett.43, 1566 (1979)

    work page 1979

  4. [4]

    Schechter and J

    J. Schechter and J. W. F. Valle, Neutrinoless Double beta Decay in SU(2) x U(1) Theories, Phys. Rev. D25, 2951 (1982)

    work page 1982

  5. [5]

    On the Quantitative Impact of the Schechter-Valle Theorem

    M. Duerr, M. Lindner, and A. Merle, On the Quantitative Impact of the Schechter-Valle Theorem, JHEP06, 091, arXiv:1105.0901 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv

  6. [6]

    Agostini, F

    M. Agostini, F. F. Deppisch, and G. Van Goffrier, Prob- ing the mechanism of neutrinoless double-beta decay in multiple isotopes, JHEP02, 172, arXiv:2212.00045 [hep- ph]

    work page arXiv

  7. [7]

    Gr´ af, M

    L. Gr´ af, M. Lindner, and O. Scholer, Unraveling the 0νββ decay mechanisms, Phys. Rev. D106, 035022 (2022), arXiv:2204.10845 [hep-ph]

    work page arXiv 2022

  8. [8]

    M. Doi, T. Kotani, H. Nishiura, and E. Takasugi, The En- ergy Spectrum and the Angular Correlation in the Beta Beta Decay, Prog. Theor. Phys.70, 1353 (1983)

    work page 1983

  9. [9]

    Technical design and performance of the NEMO3 detector

    R. Arnoldet al., Technical design and performance of the NEMO 3 detector, Nucl. Instrum. Meth. A536, 79 (2005), arXiv:physics/0402115

    work page internal anchor Pith review Pith/arXiv arXiv 2005

  10. [10]

    Probing New Physics Models of Neutrinoless Double Beta Decay with SuperNEMO

    R. Arnoldet al.(SuperNEMO), Probing New Physics Models of Neutrinoless Double Beta Decay with SuperNEMO, Eur. Phys. J. C70, 927 (2010), arXiv:1005.1241 [hep-ex]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  11. [11]

    Sensitivity of NEXT-100 to neutrinoless double beta decay

    J. Mart´ ın-Alboet al.(NEXT), Sensitivity of NEXT- 100 to Neutrinoless Double Beta Decay, JHEP05, 159, arXiv:1511.09246 [physics.ins-det]

    work page internal anchor Pith review Pith/arXiv arXiv

  12. [12]

    PandaX-III: Searching for Neutrinoless Double Beta Decay with High Pressure $^{136}$Xe Gas Time Projection Chambers

    X. Chenet al., PandaX-III: Searching for neutrinoless double beta decay with high pressure 136Xe gas time pro- jection chambers, Sci. China Phys. Mech. Astron.60, 061011 (2017), arXiv:1610.08883 [physics.ins-det]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  13. [13]

    Hikidaet al., AXEL: High-pressure xenon gas TPC for neutrinoless double beta decay search, Nucl

    J. Hikidaet al., AXEL: High-pressure xenon gas TPC for neutrinoless double beta decay search, Nucl. Instrum. Meth. A1080, 170706 (2025)

    work page 2025

  14. [14]

    A. E. Chavarriaet al., Snowmass 2021 White Paper: The Selena Neutrino Experiment, inSnowmass 2021(2022) arXiv:2203.08779 [physics.ins-det]

    work page arXiv 2021

  15. [15]

    T. Li, S. Wang, Y. Chen, K. Han, H. Lin, K. Ni, W. Wang, Y. Xu, and A. Zou, Signal identification with Kalman Filter towards background-free neutrinoless dou- ble beta decay searches in gaseous detectors, JHEP06, 106, arXiv:2102.08221 [physics.ins-det]

    work page arXiv

  16. [16]

    Novellaet al.(NEXT), Demonstration of neutrinoless double beta decay searches in gaseous xenon with NEXT, JHEP09, 190, arXiv:2305.09435 [nucl-ex]

    P. Novellaet al.(NEXT), Demonstration of neutrinoless double beta decay searches in gaseous xenon with NEXT, JHEP09, 190, arXiv:2305.09435 [nucl-ex]

    work page arXiv

  17. [17]

    Kekicet al.(NEXT), Demonstration of background rejection using deep convolutional neural networks in the NEXT experiment, JHEP01, 189, arXiv:2009.10783 [physics.ins-det]

    M. Kekicet al.(NEXT), Demonstration of background rejection using deep convolutional neural networks in the NEXT experiment, JHEP01, 189, arXiv:2009.10783 [physics.ins-det]. 7

    work page arXiv 2009

  18. [18]

    M. Doi, T. Kotani, H. Nishiura, and E. Takasugi, DOU- BLE BETA DECAY, Prog. Theor. Phys.69, 602 (1983)

    work page 1983

  19. [19]

    Scholer, J

    O. Scholer, J. de Vries, and L. Gr´ af,νDoBe — A Python tool for neutrinoless double beta decay, JHEP 08, 043, available athttps://github.com/OScholer/ nudobe, arXiv:2304.05415 [hep-ph]

    work page arXiv

  20. [20]

    M. Asai, A. Dotti, M. Verderi, and D. H. Wright (Geant4), Recent developments in Geant4, Annals Nucl. Energy82, 19 (2015)

    work page 2015

  21. [21]

    Altenm¨ ulleret al., REST-for-Physics, a ROOT-based framework for event oriented data analysis and combined Monte Carlo response, Comput

    K. Altenm¨ ulleret al., REST-for-Physics, a ROOT-based framework for event oriented data analysis and combined Monte Carlo response, Comput. Phys. Commun.273, 108281 (2022), arXiv:2109.05863 [physics.comp-ph]

    work page arXiv 2022

  22. [22]

    Qu and L

    H. Qu and L. Gouskos, ParticleNet: Jet Tagging via Particle Clouds, Phys. Rev. D101, 056019 (2020), arXiv:1902.08570 [hep-ph]

    work page arXiv 2020

  23. [23]

    Mart´ ınez-Varaet al.(NEXT), Reconstructing neu- trinoless double beta decay event kinematics in a xenon gas detector with vertex tagging, JHEP07, 170, arXiv:2502.10198 [hep-ex]

    M. Mart´ ınez-Varaet al.(NEXT), Reconstructing neu- trinoless double beta decay event kinematics in a xenon gas detector with vertex tagging, JHEP07, 170, arXiv:2502.10198 [hep-ex]

    work page arXiv

  24. [24]

    P. Herrero-G´ omezet al.(NEXT), Ba +2 ion trapping us- ing organic submonolayer for ultra-low background neu- trinoless double beta detector, Nature Commun.13, 7741 (2022), arXiv:2201.09099 [hep-ex]

    work page arXiv 2022

  25. [25]

    Imaging individual barium atoms in solid xenon for barium tagging in nEXO

    C. Chamberset al.(nEXO), Imaging individual barium atoms in solid xenon for barium tagging in nEXO, Nature 569, 203 (2019), arXiv:1806.10694 [physics.ins-det]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  26. [26]

    Adamset al.(NEXT), Sensitivity of a tonne- scale NEXT detector for neutrinoless double beta de- cay searches, JHEP2021(08), 164, arXiv:2005.06467 [physics.ins-det]

    C. Adamset al.(NEXT), Sensitivity of a tonne- scale NEXT detector for neutrinoless double beta de- cay searches, JHEP2021(08), 164, arXiv:2005.06467 [physics.ins-det]

    work page arXiv 2005

  27. [27]

    A. E. Chavarria, Background rejection in highly pixe- lated solid-state detectors, AIP Conf. Proc.2908, 100002 (2023), arXiv:2212.05012 [physics.ins-det]

    work page arXiv 2023

  28. [28]

    Kˇ riˇ z´ ak (SuperNEMO), Reconstruction of Complex Particle Trajectories in the SuperNEMO Detector, PoS EPS-HEP2025, 190 (2026)

    T. Kˇ riˇ z´ ak (SuperNEMO), Reconstruction of Complex Particle Trajectories in the SuperNEMO Detector, PoS EPS-HEP2025, 190 (2026)

    work page 2026

  29. [29]

    standard

    A. Stuart, K. Ord, and S. Arnold,Kendall’s Advanced Theory of Statistics, Volume 2A, Classical Inference and the Linear Model(Wiley, 2008). Supplemental: Statistical tests for multiple simple hypotheses The hypothesesH i described in this manuscript take the form of simple hypotheses, i.e., hypotheses which have no degrees of freedom and thus each specifi...

    work page 2008